Question: Simplify the following expression: $\dfrac{15q^3}{5q}$ You can assume $q \neq 0$.
$ \dfrac{15q^3}{5q} = \dfrac{15}{5} \cdot \dfrac{q^3}{q} $ To simplify $\frac{15}{5}$ , find the greatest common factor (GCD) of $15$ and $5$ $15 = 3 \cdot 5$ $5 = 5$ $ \mbox{GCD}(15, 5) = 5 $ $ \dfrac{15}{5} \cdot \dfrac{q^3}{q} = \dfrac{5 \cdot 3}{5 \cdot 1} \cdot \dfrac{q^3}{q} $ $\phantom{ \dfrac{15}{5} \cdot \dfrac{3}{1}} = 3 \cdot \dfrac{q^3}{q} $ $ \dfrac{q^3}{q} = \dfrac{q \cdot q \cdot q}{q} = q^2 $ $ 3 \cdot q^2 = 3q^2 $